Download Quantitative inheritance

Quantitative inheritance
Qualitative and Quantitative traits,
Variation in traits, polygenic model
Lecture 5
Aims
• To equip students with knowledge
on the inheritance of polygenic traits
Learning Objectives
• By the end of the topic, students should
be able to
• Differentiate quantitative traits from qualitative traits
• Describe traits of importance in farm animals
• Explain the polygenic model
• Describe and understand the basis of quantitative
variation and its measures
• Describe terms values and means
• Explain breeding values and genotypic values
• Compute values for various terms
DNA on chromosome
(number per cell nucleus are species specific)
Genes
(control all traits in animals and plants)
Qualitative (major) traits
Quantitative (polygenic) traits
Genotype
(a collection of alleles an individual has in its genome)
Interaction between alleles at a locus and between genes at
different loci influence inheritance mode
Phenotype
(what the animal or plant looks like with respect to a particular trait
or a composite combination of traits)
Traits of interest in farm animals
• Many traits in farm animals are
measured on a continuous scale
• And are termed quantitative traits
• In contrast to traits that fall into
distinct classes
• Termed qualitative or discrete traits
Types of traits
Traits
Qualitative
Quantitative
Controlled by single or few genes
Each gene has a major effect
Controlled by many genes,
each with a small effect
(influence)
No environmental influence
Influenced by environment
Discrete in expression
Continuous in expression
Observed
Measured rather than observed
Described by proportions
Described by statistics
e.g. coat colour, hornness, shape of e.g. body weight, milk yield,
ear (inherited in a simple mendelian
egg production, fibre content,
fashon)
power
Of economic importance
Quantitative traits
Are also called polygenic, controlled by
many loci
Each has little additive effect to the
expression (animal performance)
Are mostly complex in inheritance
With many biochemical pathways and
proteins, enzymes involved
And measured on a continuous scale (as
quantities)
Polygenic model
As the number of genes controlling a trait
increases, the distribution of genetic
effects become normal
Quantitative traits are assumed to be
controlled by many genes at many loci:
thus the polygenic model
This can be described by looking at the
variation ~ shown in following slides
Assumptions behind following slides
•
To illustrate discontinuous variation caused by
genetic segregation as it is translated into
continuous variation of metric traits
1. Consider any locus, each with two alleles ~ i.e. two
forms of a gene, with equal gene frequency
2. There is no dominance of one allele at each locus
3. Then the dominant allele adds 1 unit to the
measurement of a trait, recessive allele adds -1 unit
4. Loci are not linked, each loci having equal effect on
phenotype (trait) measure
In fact, all these assumptions are not true
For a trait controlled by one locus
genotypic value of quantitative trait~
single locus model
 Locus 1 with 2 alleles A, a
 Allele A has value +1; allele a has value -1
 Genotypic classes and values are as below
Genotypic
class
AA
genotypic value
1 + 1
+2
Aa
1 + -1
0
aa
-1 + -1
-2
Traits are discrete, comprised only few classes
Example of determining genotypic
value of quantitative trait, single locus
Consider weaning weight in pigs at 15 weeks
Mean weight = 20 kg
Locus 1 with 2 alleles A, a
Genotype
Mean + genotypic value
= weight
AA
20 + 2
22
Aa
20 + 0
20
Aa
20 + 0
20
aa
20 + -2
18
With respect to locus 1 the pigs could be any of the three genotypes
2
2
1.5
1.5
Frequency
Frequency
Single locus model, only three classes
1
0.5
1
0.5
0
18
20
Value, wt
22
0
-2
0
Value
2
Two locus model
Consider trait controlled by 2 Loci, each
with 2 alleles A, a and B, b
A and B have value +1; a and b values -1
Genotypic value for Bs, As as in above
Genotype
Genotype Genotypic value
Weight
AABB
24
AABb
22
AaBB
22
BB
+2
Bb
0
AaBb
20
AAbb
20
bb
-2
aaBB
20
Aabb
18
aabB
18
aabb
16
With combined effect of locus 1 & 2, the
range of genotypes widens
Two locus model
AB
Ab
aB
ab
AB
AABB
AABb
AaBB
AaBb
Ab
AABb
AAbb
AaBb
Aabb
aB
AaBB
AaBb
aaBB
aaBb
ab
AaBb
Aabb
aaBb
aabb
Two locus model, genotype values
AABB
+4
AABb
+2
AaBB
+2
AaBb
0
AABb
+2
AAbb
0
AaBb
0
Aabb
-2
AaBB
+2
AaBb
0
aaBB
0
aaBb
-2
AaBb
0
Aabb
-2
aaBb
-2
aabb
-4
Example of determining genotypic
value of quantitative trait, two loci
Consider Locus 2 with 2 alleles B, b
AaBb
AaBb
aabB
AaBb
AaBB
aabB
AAbb
AABb
aabb Aabb aaBB
16
AABb
18
20
5
Frequency
Aabb AaBb
6
3
2
AaBB AABB
22
4
24
1
0
16
18
20
22
24
Weight
-4
-2
0
Genetic effects
+2
+4
-4
-2
0
+2
Trait starts to appear
quantitative
+4
Example of determining genotypic
value of quantitative trait, three loci
Consider Locus 3 with 2 alleles C, c
With combined effect of locus 1, 2 & 3,
the range of genotypes and phenotypes
widens even further
Majority animals tend to be at the middle
of the range and the distribution of the
phenotype tend to be almost normal
Number of genotype
combinations
n
2n
Number of gene pairs with 2
alleles
Number of possible gametes
3n
Number of possible genotypes
alleles A & a has n = 1; therefore, 2 possible
gametes A & a; 3 possible genotypes AA, Aa & aa
Check excel for genotypes and gametes
Possible gametes and genotypes~
Can be illustrated through Punnet Square
• 2 alleles, 1 loci
• ~ 3 genotypes
possible
2 loci, each with 2 alleles
~ 9 genotypes possible
A
a
A
AA
Aa
a
Aa
aa
AB
Ab
aB
ab
AB
AABB
AABb
AaBB
AaBb
Ab
AABb AAbb AaBb
Aabb
aB
AaBB
AaBb
aaBB
aaBb
ab
AaBb
Aabb
aaBb
aabb
Sharp rise in genotypes and
gametes as number of loci
increase
1200000
4E+09
3.5E+09
1000000
3E+09
800000
2.5E+09
600000
2E+09
1.5E+09
400000
1E+09
200000
500000000
0
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Number of gene pairs
No of gametes
No of genotypes
Frequency
Example of determining genotypic
value of quantitative trait, three loci
20
18
16
14
12
10
8
6
4
2
0
14
16
18
20
22
24
26
Weight
-6
-4
-2
0
+2
+4
+6
Work out 27
genotypes
Quantitative traits are affected by more than three loci,
thus produce a smooth normal distribution
Assignment
• Work out four loci model and
determine
• Genotype values
• Frequency for each genotype
• Plot the distribution
Polygenic model
As the trait get controlled by numerous
loci, each with multiple alleles
The number of genotypic classes
becomes large,
and the genotypic values become
normally distributed
How are these traits inherited
 The combined effect of the alleles at many loci
make up genotypic value of an individual
 Genotypic value = the value of the animal’s
genes to its own performance
 During reproduction, an animal passes an allele
from each locus to its offspring (progeny)
 Which one is passed to is at random
 This makes each offspring to inherit a different set
of alleles from the other
 Thus each offspring will have different genotypic
value due to this random sampling of alleles from
each parent – the Mendelian sampling
How are these traits inherited
It is this transmission of alleles from parents
to offspring and the different set of
combination that leads to observed
variation in a trait
Assumptions behind not always true
•
Consider any locus, each with two alleles ~ i.e. two forms
of a gene, with equal gene frequency
•
Fact, > 2 alleles exist, each with different frequencies
•
Dominance effect takes place
•
•
Loci can be linked
Each loci can be with different effect
•
There is no dominance of one allele at each locus
•
Then the dominant allele adds 1 unit to the
measurement of a trait, recessive allele adds -1 unit
Loci are not linked, each loci having equal effect on
phenotype (trait) measure
•
Check for effect of dominance in Animal Breeding
software~ Inheritance of quantitative traits
Continuous variation expressed
• Variation of this sort, without natural
discontinuities, is called
Continuous variation
• Characters or traits that exhibit continuous
variation are called
Quantitative traits or metric characters
– Since their study depend on measurement instead of
counting
• The brach of genetics concerned with metric
characters is called
Quantitative or biometrical genetics
• Since segregation of genes cannot be followed
individually, mode of inheritance is called
Quantitative inheritance
Summary: polygenic model
As the number of genes controlling a trait
increases, the distribution of genetic
effects become normal
Quantitative traits are assumed to be
controlled by many genes at many loci:
thus the polygenic model
Effect of the environment
An individual deviates from its genotypic
value due to environmental effects
These include
Nutrition
Climate
Disease
Random measurement error
Environmental effects
The effect of the environment on a
quantitative trait for a group of animals
also tend to be normally distributed
 This assumes random environmental effects. Systematic
environmental effects, e.g. year, season, housing differences,
feed type, sex, etc can be accounted for
Phenotypes
An individual inherits genetic effects and
receives environmental effects
The combined effect of these make up
the phenotype
Phenotype is therefore, the sum of
genetic effects and environmental
effects
Phenotype  Genotype  Environment
P GE
Phenotypic effects
If P is expressed as deviation from group
mean
An individual’s deviation in phenotype is
due to the sum of its deviation in genetic
and environmental effects
Phenotypic effects
Animal
Population
Mean, kg
G
E
P
1
40
+6
+6
52
2
40
+2
+14
56
3
40
-2
-4
34
4
40
+6
-2
44
5
40
-8
+4
36
Mean = average value of genes all individuals in a
population have in common, plus the average level
of management
Phenotypic effects
8
4
2
0
-2
1
2
3
4
20
5
Phenotypic effects
Genotypic value
6
-4
-6
-8
-10
Animal
15
10
5
0
1
2
3
Environmental deviations
-5
16
14
-10
12
Animal
10
8
6
4
2
0
-2
-4
1
2
3
-6
Animal
4
5
4
5
All effects
Phenotypic variation
When a large number of animals are
measured, you get variation in the
phenotypic values for a trait
Just as P = G + E, Variance in P is the sum of variance in
genotypic effects and variance in environmental effects
Phenotypic variation
Due to large number of effects on the
trait, that is why variation distribution is
normal
When you put all the effects together,
you get normally distributed observations
Measures of variation
100
80
70
60
Frequency
 As quantitative
traits are (usually)
normally
distributed
 They can be
described by the
measure of the
central tendency
(mean) and its
variance
(standard
deviation)
90
50
40
30
20
10
0
350
375
400
425
450
475
500
Weaning weight
525
550
575
600
625
More
Normality: a review
• It is bell curve
• One of many distributions
• Majority observations tend to be at
the middle
• Fewer observations are at extreme
ends
• Most traits in livestock are normally
distributed
Summary on variation in
quantitative traits
Quantitative traits show a normal
distribution
Due to
Underlying genetic distribution, attributed to
polygenic trait model
An underlying environmental distribution
It is the genetic variance in quantitative
traits that is of importance in animal
breeding
It allows selection for genetically superior
animals
Properties of a population with metric
characters
• In quantitative traits, properties we
can observe include
• Means
• Variances
• Co-variances
Based on these properties
• Variance can be split into components
• Through natural subdivision of population into
families
• And use that to measure degree of
resemblance between relative
• So that observations made on population can be
used to predict outcome of a breeding method
• And observe impact of a breeding program
• And also to find out how observable properties of a
population are influenced by genetic and nongenetic factors
Concept of mean and variance
 Mean measures the central tendency of a
population for a particular trait
 Variance and standard deviation describes the
spread of a normally distributed population
 Mean

X
n
X
n
 Variance (Vx)
 Standard deviation (σ)
Vx 
 X
X
n 1
  Vx
2
An example
Live weight data for adult local sheep
Check in excel
An exercise
Calculate mean and variance in excel
For heart girth in sheep
And for the data on pig production at our
Students’ Farm ~ you will collect from the
Animal Recording Technician
Standard deviation (σ), what is it?
σ=1
 Describes the spread of the
distribution
σ=5
 The greater the σ, the greater
the spread
 ~68% of the measurements are
±1 σ units
σ=10
 Fewer measurements ~1% are
greater than ±3 σ from the
mean
 units
Mean and variance
Weaning Weight
Frequency
100
80
60
40
20
Mean = ~525
More
625
600
575
550
525
500
475
450
425
400
375
350
0
standard deviation = ~50
•Mean
•Describes the middle of a normal distribution
•Standard deviation describes a width of a
normal distribution
Practically expect
 Variance to differ between
flocks
 More variance in flocks kept in
a wide environment like ranch
than those kept under uniform
environment like a barn
 More variance in local than
improved strains
 More variance in unselected
than in animals that have
undergone selection
V p  VG  VE
V p  VG  VE
V p  VG  VE
VG  VA  VD  VI
Practically expect
Practically expect
Different flocks can have same mean but
different variance
Sakhula flock
SF flock
Mean, g
2.2
2.2
Variance, g2
0.04
0.36
Std, g
0.20
0.60
Simple properties of variance
 Adding a constant to each observation
(measurement) does not change the variance,
only the mean
 If X and Y are independent,
Var X  Y   Var( X )  Var(Y )
 E.g. Genetic and environmental effects, where there is no
GxE interaction
 Two unrelated traits, where they are not genetically or
environmentally correlated
Further reading
• Inheritance of quantitative traits
• In Animal Breeding software
Further explanation on terms
• ‘Values’ and ‘means’
• ‘Average effects’ and ‘breeding
values’
• Refer to Falconer Chapter 7
• And, Inheritance of quantitative traits
• In Animal Breeding software
• To be covered in detail in Applied Animal
Breeding
Summary of terms: Value
• Value is basically
what was
expressed as
Genotype value
• Recall
• Much as we
measure the P, our
interest is the G
P GE
V p  VG  VE
Value
• Recall genotypes and their frequencies
under HW equilibrium
Genotype
Frequency
Gij=Genotypic
expression
Genotypic
value
Yij=Phenotypic
expression
AA
p2
G11
+a
Y11
Aa
2pq
G12
d
Y12
aa
q2
G22
-a
Y22
Mean genotypic value of two
homozygotes
• Is equal to zero
• Genotypic value is defined as deviation
of the phenotype from the average of
the two homozygous phenotypes
• Recall, this is the value of genes to the
animal itself
– Mid-point between two homozygotes serves
as an origin with zero value
• Hence, genotypic values are measured as
deviation from the mid-point
A2A2
-a
A1A2
0
d
A1A1
Genotype
+a
Genotypic
values
Genotypic value of heterozygote ~ d
• Determines the degree of dominance
• When
• d=0, means there is no dominance
• Genes are just additive (additive case)
A2A2
-a
A1A2
0
d
A1A1
Genotype
+a
Genotypic
values
Genotypic value of heterozygote ~ d
• Determines the degree of dominance
• When
• d=a, means there is complete dominance
• A1 is dominant over A2 ~ d is positive
• A2 is dominant over A1 ~ d is negative
A2A2
-a
0
A1A2
A2A2
-a
-d
0
A1A2
A1A1
Genotype
+a
d
Genotypic
values
A1A1
Genotype
+a
Genotypic
values
Genotypic value of heterozygote ~ d
• Determines the degree of dominance
• When
• 0<d<a, means there is partial dominance
A2A2
-a
0
A1A2
A1A1
Genotype
d
+a
Genotypic
values
Genotypic value of heterozygote ~ d
• Determines the degree of dominance
• When
• d>a, means there is over dominance
A1A1 A1A2
A2A2
-a
• The degree of
dominance
• Is expressed as
+a
0
d d
a
d
Genotype
Genotypic
values
Example 7.1 in Falconer
• Go through Example 7.1 in Falconer
Mean
Genotype
AA
Aa
aa
Frequency Gij=Genotypic
expression
p2
2pq
q2
Genotypic
value
Yij=Phenotypic
expression
+a
d
-a
Y11
Y12
Y22
G11
G12
G22
• Mean genotypic value is obtained by
f G
ij
ij
• Where
• Fij is genotype frequency
• Gij if genotypic value
Mean
Genotype
Frequency
Genotypic
value
Freq x Value
AA
Aa
aa
p2
2pq
q2
+a
d
-a
p2a
2pqd
-q2a
a(p-q)+2dpq
f G
ij
ij
 mean  sumofcolumns  
•Note that the sum is the mean since the sum is
divided by 1, 1 being equal to sum of three
genotype frequencies
•i.e. p2+2pq+q2 = 1
Derivation of the mean
   fijGij  p a  2 pqd  q (a)
2
2
 p a  q a  2 pqd
2

2

 a p  q  2 pqd
2
2
 a p  q p  q  2 pqd
 a p  q  2 pqd
Contribution of any locus to
population mean
• Includes
– A term associated with homozygotes
– a(p-q)
– A term associated with heterozygotes
– 2pqd
• Check Falconer for contribution and mean
under
•
•
•
•
No dominance
Complete dominance
When A1 were fixed in a population (p=1)
When A2 were fixed in a population (q=1)
Contribution to Mean from many loci
• Assuming no epistasis
   a p  q   2 pqd
Go through example 7.1 and 7.2 in
Falconer
• Note
• Under normal environment
• Mean environmental deviation is zero
• Hence, population mean refers to
phenotypic or genotypic values
• Values are in unit of measure
• Check excel to see how gene
frequency influences the mean
Go through example 7.1 in Falconer
Example 7.1 in Falconer
Weight, g
Mean
under
differing
gene
frequencie
s, p
Deviation Mean
0.5
AA
Actual measure
Aa
aa
Mean
a
Values
d
(a)
14
12
6
10
4
2
-4
1
14
14
4
9
5
5
-5
2.5
14
14
14
4
15
3
4
4
4
9
9
9
5
5
5
-5
6
-6
-5
-5
-5
-2.5
3
-3
Complete, positive
11.5 dominance
Complete,
negative
6.5 dominance
12 Over dominance
6 Over dominance
0
No dominance,
mean determined
10 by gene frequency
14
10
6
10
4
0
-4
11 Partial dominance
Average effect and breeding value
• With respect to transmission of value from
parents to offspring
• Parents pass their genes and not genotypes
• Genotypes are created afresh in each generation
• Genotype values are therefore, not transmitted
• A new measure of values that refer to
genes and not genotypes is needed
– This new value associated with genes and not
genotypes is the
• Average effect
Basis of inheritance
Average effect of a particular gene
(allele)
• The mean from the population
mean of individuals which received
that allele from one parent, the
allele received from the other
parent having come at random
from the population
• This new value allows us to assign a
breeding value to individuals
Breeding value
• A value associated with the genes
carried by an individual and
transmitted to its offspring
• This is value of genes to the animal
offspring
• That is, genotypic value of animal’s
future progeny
Breeding value
• Since it is only genes that are transmitted
to offspring,
• It is therefore, the average effects of
parents’ genes that determine the mean
genotypic value of its progeny
• The value of the individual, judged by the
mean value of its progeny is the breeding
value of the individual
Breeding value and Genetic value
• Genetic value
• Value of genes to the individual itself
• Includes dominant deviation that is not passed to
offspring
• Since each passes one allele
• Breeding value
• Value of genes to progeny
• Sum of average effects of the individual’s alleles
carried
• Average effect of an allele depends on frequency
of the allele in a population
Breeding value, example
• Under a single locus model
• If αA1= 10 and αA2= -10
• BVA1A1= 10 + 10
=
• BVA1A2= 10 + -10
=
• BVA2A2= -10 + -10
=
20
0
-20
• Breeding values = the sum of the average
effect of the individual’s alleles (α)
Breeding value, example
• Under a single locus model
If αA1= 5 and αA2= -2
• BVA1A1= 5 + 5
• BVA1A2= 5 + -2
• BVA2A2= -5 + -5
=
=
=
10
3
-10
• Breeding values = the sum of the average
effect of the individual’s alleles (α)
G, BV and dominance
• Since BVs are sum of average effects of
genes
• The heterozygote is always halfway between the
two homozygotes
• Irrespective of dominance
• with no dominance
• Genetic and breeding values are equal
• With some dominance
• Genetic and breeding values differ
• See details in Excel
Breeding value terms
• Also referred to as
• Additive genotype
• Variation in breeding values also referred to as
• Additive effects of genes
• Breeding value in livestock is the genetic merit of
an animal, used to rank animals and is an aid to
selection
• The difference between genotypic value, G and
breeding value, A of a particular genotype is
known as dominance deviation, D
Summary
• Breeding values are expressed as a
deviation of the population mean
• with the population mean dependent on
genotypic values and frequencies
• dominance G With no dominance
G=A, with dominance G≠A
• Animals with a rare allele will have a
larger breeding value
• either positive or negative BV
Summary
• Breeding values are additive
• BVs are used to predict progeny
performance
• By estimating expected genetic value
coming from one parent used in
breeding
• Most likely the sires ~ details in software on
Inheritance of animal breeding
Point to note
• Breeding values always halved when
predicting progeny performance
• Referred to as transmitting ability
• Remember
• BV represents the sum of average effects of two
alleles
– Only one of which is passed on
• These concepts relating genetic to BV
could be extended from a single locus
model to a multiple locus model